The rheological properties of polymer melts depend strongly on the underlying molecular structure : molecular weight, molecular weight distribution, and long chain branching. It is of considerable importance, both fundamental and practical, to relate the molecular architecture to polymer melt theology. The focus of the present work is in extracting a measure of polydispersity from theological data. Various polydispersity measures that have been proposed in the literature are critically examined and their limitations are pointed out. New measures of polydispersity are proposed that overcome these limitations. The evaluation of the various polydispersity measures is performed by reference to theology fundamentals, with model calculations and examples drawn from industrial practice. The issues of eliminating molecular weight and temperature effects in characterizing polydispersity are comprehensively addressed. The presence of small levels of long chain branching in an otherwise linear polymer alters most of these measures of polydispersity dramatically, while no detectable change appears in the molecular weight distribution obtained using a gel permeation chromatograph. It is demonstrated that the polydispersity measures proposed in the present work, and which are extracted from frequency response data in the linear viscoelastic region, can be used reliably to characterize polydispersity in polymer melts.